Weight Painting/Deform in shoulders
I'm very inexperienced when it comes to rigging, but I'll try to point you in the right direction, your rig lacks the collarbones, as scuh you expect their behaviour to be included in the shoulder.


this guys right here.

I think doing your own rig can be agreat learning experience and you can also tailor it to your own needs, I'd suggest importing the rigify rig and studying it a bit to see how it works, also looking at a few anatomical references to understand where you should insert the bones into your model.

Also skinning is very trial and error, try animating different movements and seeing how your model reacts, most high end rigs have corrective blendshapes which iron out some kinks when doing certain movements, or bulge out muscle when flexing, many ways to skin a cat.